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arXiv:1405.0522 · Physical Review B

Dynamic phase diagram of dc-pumped magnon condensates

Scott A. Bender, R. A. Duine, Arne Brataas, Yaroslav Tserkovnyak

Published Sep 12, 2014• 57 citations
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Abstract

We study the effects of nonlinear dynamics and damping by phonons on a system of interacting electronically pumped magnons in a ferromagnet. The nonlinear effects are crucial for constructing the dynamic phase diagram, which describes how ``swasing'' and Bose-Einstein condensation emerge out of the quasiequilibrated thermal cloud of magnons. We analyze the system in the presence of magnon damping and interactions, demonstrating the continuous onset of stable condensates as well as hysteretic transitions.

DOI
10.1103/physrevb.90.094409

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We study the effects of nonlinear dynamics and damping by phonons on a system of interacting electronically pumped magnons in a ferromagnet. The nonlinear effects are crucial for constructing the dynamic phase diagram, which describes how ``swasing'' and Bose-Einstein condensation emerge out of the quasiequilibrated thermal cloud of magnons. We analyze the system in the presence of magnon damping and interactions, demonstrating the continuous onset of stable condensates as well as hysteretic transitions.
An equation for the dynamics of a Bose-Einstein condensate of magnons in a ferromagnetic film is presented, derived from quantum-mechanical theory. The main interactions affecting the evolution of the condensed state are considered. The transition from the equation for the annihilation operator of condensed magnons to an autonomous system of first-order differential equations describing their amplitude and phase is made. Phase trajectories of such a system were studied by constructing phase portraits and determining the stability of stationary points.
We propose a stabilizing mechanism for the Bose-Einstein condensation (BEC) of interacting magnons in ferrimagnets and ferromagnets. By studying the effects of the magnon-magnon interaction on the stability of the magnon BEC in a ferrimagnet and two ferromagnets, we show that the magnon BEC remains stable even in the presence of the magnon-magnon interaction in the ferrimagnet and ferromagnet with a sublattice structure, while it becomes unstable in the ferromagnet without a sublattice structure. This indicates that the existence of a sublattice structure is the key to stabilizing the BEC of interacting magnons, and the difference between the spin alignments of a ferrimagnet and a ferromagnet is irrelevant. Our result can resolve a contradiction between experiment and theory in the magnon BEC of yttrium iron garnet. Our theoretical framework may provide a starting point for understanding the physics of the magnon BEC including the interaction effects.
We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate (BEC) prepared in a room temperature yttrium-iron-garnet (YIG) magnetic film. The magnon BEC is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-resolved Brillouin light scattering (BLS) spectroscopy in the area of the BLS laser focus. It has been found that local laser heating in the center of the condensate decreases the density of the magnon BEC in the steady-state pump regime and it enhances the temporal decrease of the freely evolving magnon condensate after the termination of the pumping pulse, but it does not alter the relaxation dynamics of the gaseous magnon phase. This phenomenon is understood as the appearance of a magnon supercurrent within the condensate due to a temperature-gradient induced phase gradient in the condensate. Bose-Einstein condensation [1] can be achieved either by decreasing the temperature of a boson gas [2] or by increasing its density. The latter method is especially applicable to g ases of weakly interacting quasi-particles such as excitons [3] , polaritons [4, 5], photons [6], and magnons [7, 8]. When a spin system is pumped, and when the injected magnons thermalize through scattering processes conserving both their number and the total energy, a Bose-Einstein condensate (BEC) may be formed at the lowest energy state of the energy-momentum spectrum even at room temperature conditions of the magnetic film carrying the magnons [8, 9]. As the condensed magnon phase is localized in the global energy minimum, its group velocity is exactly zero and no energy transport can be associated with the magnon BEC. The situation can change, when a magnon supercurrent driven by a gradient in the phase of the wavefunction of a magnon condensate can be excited. Such a phase gradient can be induced by, e.g., a potential gradient or a temperature gradient. However, the dynamics of magnon condensates in such a gradient is still terra incognita. Here we provide experimental insight into the evolution of a magnon BEC in a thermal gradient generated by local laser heating. We show that such a heating influences both the steady-state characteristics and the transitional behavior of the magno n BEC, which can be understood using the concept of a magnon supercurrent. We study the temporal evolution of a magnon BEC in a single-crystal yttrium iron garnet (YIG, Y3Fe5O12) film by
Research on the phase transition and phase diffusion between the Mott-insulator and superfluid phase has not yet been done extensively for the case of magnons. In this thesis we start from a model Hamiltonian for an easy-plane magnetic insulator and construct the phase diagram describing the transition between the Mott insulator and superfluid phase. Finally, we consider phase diffusion of the Bose-Einstein condensate in the superfluid phase and find that phase diffusion indeed occurs in a finite-sized system.
Abstract The spontaneous emergence of coherence is a defining feature of multibody quantum systems, underlying phenomena from superconductivity to quantum information processing. Although Bose–Einstein condensates provide a unique setting for studying this process, direct observation of how a condensate acquires a coherent global phase has remained challenging. Here we provide evidence of spontaneous phase formation in a magnon Bose–Einstein condensate. Using a phase-referenced detection technique, we track the phase of the condensate coherent state relative to an external reference, revealing how an initially incoherent magnon gas thermalizes and undergoes a spontaneous transition into a coherent quantum state with a well-defined macroscopic phase. This observation provides evidence of spontaneous symmetry breaking in a quasiparticle condensate, confirming a central prediction of Bose–Einstein condensation theory that extends across diverse quantum systems.